Câu 3: Giải các phương trình sau bằng cách đưa về dạng ax+b=0

1. a, \(\frac{5x-2}{3}=\frac{5-3x}{2}\); b, \(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)

c, \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\); d, \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)

e, \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\); f, 4 (0,5-1,5x)=\(\frac{5x-6}{3}\)

g, \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\); h, \(\frac{x+4}{5}.x+4=\frac{x}{3}-\frac{x-2}{2}\)

i, \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\); k, \(\frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5\)

m, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\); n, \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right).\frac{1}{3}\left(x+2\right)\)

p, \(\frac{x}{3}-\frac{2x+1}{6}=\frac{x}{6}-x\); q, \(\frac{2+x}{5}-0,5x=\frac{1-2x}{4}+0,25\)

r, \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\); s, \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{6}\)

t, \(\frac{2x-8}{6}.\frac{3x+1}{4}=\frac{9x-2}{8}+\frac{3x-1}{12}\); u, \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{3}+\frac{2x-1}{12}\)

v, \(\frac{5x-1}{10}+\frac{2x+3}{6}=\frac{x-8}{15}-\frac{x}{30}\); w, \(\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x\frac{x-3}{2}}{5}-x+1\)

Bài 1: rút gọn phân thức

a) \(\frac{14xy^2\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)

b) \(\frac{8xy\left(3x-1\right)^2}{12x^3\left(1-3x\right)}\)

c) \(\frac{20x^2-45}{\left(2x+3\right)^2}\)

d) \(\frac{5x^2-10xy}{2\left(2y-x\right)^3}\)

e) \(\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)

f) \(\frac{9-\left(x+5\right)^2}{x^2+4x+4}\)

g) \(\frac{32x-8x^2+2x^3}{x^3+64}\)

h) \(\frac{5x^3+5x}{x^4-1}\)

Bài 2: Quy đồng mẫu thức của các phân thức sau

a) \(\frac{7x-1}{2x^2+6x};\frac{5-3x}{x^2-9}\)

b) \(\frac{x+1}{x-x^2};\frac{x+2}{2-4x+2x^2}\)

c) \(\frac{4x^2-3x+5}{x^3-1};\frac{2x}{x^2+x+1};\frac{6}{x-1}\)

d) \(\frac{7}{5x};\frac{4}{x-2y};\frac{x-y}{8y^2-2x^2}\)

bài tập. Giải các pt

1, \(\frac{5}{x-2}+\frac{6}{3-4x}=0\)

2,\(\frac{x+1}{x-2}=\frac{1}{x^2-4}\)

3,\(\frac{x+2}{x}-\frac{x^2+5x+4}{x\left(x+2\right)}=\frac{x}{x+2}\)

4,\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)

5,\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)

6,\(\frac{x+1}{x}+\frac{1}{x+1}=\frac{2x-1}{2x^2+2}\)

7,\(\frac{2}{x+1}-\frac{3x+1}{\left(x+1\right)}=\frac{1}{\left(x+1\right)\left(x-2\right)}\)

8,\(\frac{4}{x^2+2x-3}=\frac{2x-5}{x+3}-\frac{2x}{x-1}\)

9,\(\frac{3}{x^2+x-2}-\frac{1}{x-1}=\frac{-7}{x+2}\)

Thực hiện phép tính:

a)\(\frac{2x+6}{3x^2-x}:\frac{x^2+3x}{1-3x}\)

b)\(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)

c)\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)

d)\(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)

e)\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)

f)\(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)

g)\(\frac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\frac{2}{x^2+3}+\frac{1}{x+1}\)

Bài 1. Giải các phương trình sau

1) \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}-2x\)

2) \(\frac{x-3}{5}=6-\frac{1-2x}{3}\)

3) \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)

4) \(\frac{2x+3}{3}=\frac{5-4x}{2}\)

5) \(\frac{5x+3}{12}=\frac{1+2x}{9}\)

6) \(x-\frac{x+1}{3}=\frac{2x+1}{5}\)

7) \(\frac{3\left(x-3\right)}{4}+\frac{4x-10,5}{10}=\frac{3\left(x+1\right)}{5}+6\)

8) \(\frac{2\left(3x+1\right)+1}{4}-5=\frac{2 \left(3x-1\right)}{5}-\frac{3x+2}{10}\)

9) \(\frac{x+1}{3}+\frac{3\left(2x+1\right)}{4}=\frac{2x+3\left(x+1\right)}{6}+\frac{7+12x}{12}\)

10) \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)

Giải các  phương trình sau :

\(a,6x^2-5x+3=2x-3x\left(3-2x\right)\)

\(b,\frac{2\left(x-4\right)}{4}-\frac{3+2x}{10}=x+\frac{1-x}{5}\)

\(c,\frac{2x}{3}+\frac{3x-5}{4}=\frac{3\left(2x-1\right)}{2}-\frac{7}{6}\)

\(d,\frac{6x+5}{2}-\frac{10x+3}{4}=2x+\frac{2x+1}{2}\)

\(e,\left(x-4\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)

Giải phương trình:

1. \(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)

2. \(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)

3. \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\)

4. \(\frac{x+3}{2}-\frac{x-1}{3}=\frac{x+5}{6}+1\)

5. \(\frac{x-4}{5}-\frac{3x-2}{10}-x=\frac{2x-5}{3}-\frac{7x+2}{6}\)

6. \(\frac{\left(x+2\right)\left(x+10\right)}{3}-\frac{\left(x+4\right)\left(x+10\right)}{12}=\frac{\left(x-2\right)\left(x+4\right)}{4}\)

7. \(\frac{\left(x+2\right)^2}{8}-2\left(2x-1\right)=25+\frac{\left(x-2\right)^2}{8}\)

8.\(\frac{7x^2-14x-5}{5}=\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}\)

9. \(\frac{\left(2x-3\right)\left(2x+3\right)}{8}=\frac{\left(x-4\right)^2}{6}+\frac{\left(x-2\right)^2}{3}\)

10. \(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)

Giải các phương trình sau:

a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)

b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)

c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)

d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)

e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)

f) \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)

g)\(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)

h) \(\frac{12x+1}{6x-2}-\frac{9x-5}{3x+1}=\frac{108x-36x^2-9}{4\left(9x^2-1\right)}\)

i) \(x+\frac{1}{x}=x^2+\frac{1}{x^2}\)

j) \(\frac{1}{x}+2=\left(\frac{1}{x}+2\right)\left(x^2+2\right)\)

k) \(\left(x+1+\frac{1}{x}\right)^2=\left(x-1-\frac{1}{x}\right)^2\)